The transformations in \(\mathcal {T}\)  represent all actions that the theory allows the global agent to implement.
We can think of them as the ways in which the agent may test a theory, by applying actions that change state parameters.
For example, an explicit theory of a quantum universe may allow only for unitary operations, while a more generous theory could equip the agent with implicit large ancillas, and allow her to implement general quantum channels, state preparations and even tomography. Again the two views can be related: the latter is an effective theory derived from the unitary quantum theory, by internalizing part of the global space as belonging to the agent and her instruments, and not to the object of study (the rest of the universe) [1]}. In the context of field theories, this is discussed as emerging agency [2]}. In a superdeterministic theory, there is only one possible course of evolution for the universe, and \(\mathcal {T}\)  consists only of functions that apply it (for example \(\mathcal {T}\cong \lbrace e^{-i H t} \rbrace _t\)  where the global agent is given some choice of time).
Formally, \(\mathcal {T}\)  is a monoid of functions \(f: \Omega \rightarrow \Omega \) : it contains the identity transformation and is closed under concatenation (an associative binary operation), such that performing two actions subsequently, \(f \circ g\) , is still an allowed operation. We discuss the monoidal assumption and possible relaxations in Section .
